Write out the first eight terms of the series to show how the series starts. Then find the sum of the series or show that it diverges.

${\displaystyle \underset{n=1}{\overset{}{}}}(1-\frac{5}{4^n})$

The first eight terms are $a_1=,a_2=,a_3=,a_4=,a_5=,a_6=,a_7=,$ and $a_8=$

$($Simplify your answers.$)$